CIRCLES. 8 ABCD is a parallelogram inscribed in a circle. BC = 6, g-c = 120. Find the diameter of the circle. Test 10 Series 3. Part I [20 points)

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1 Class _ Date CIRCLES Test 10 Series 3 Part I [20 points) In problems 1-4, refer to the diagram and the informatlon given. ~-~ and ~-C are tangent to the circle. w Find the measure of LCEF. Find the measure of LD. Find the measure of ~C. B Find the measure of LEBD. 5 Find the circumference of a circle in which an 18-cm chord is 40 cm from the center. 1 2_ 3 4 D 5_ In problems 6 and 7, refer to the diagram and the information given. MAT = 150, LM = 78 6 Find the measure of LH. 7 Find the measure of LT H 8 ABCD is a parallelogram inscribed in a circle. BC = 6, g-c = 120. Find the diameter of the circle. In problems 9 and 10, refer to the diagram and the information given. c is tangent to the circle. Find AQ. B 10 Find PT. Copyright M(~Dougal, Littetl & Company T Test 10 I 213

2 Name Class Date CIRCLES (continued) Test ~l O Seri.es 3 Part II (20 points} 11 A kite with sides 12 and 5 is inscribed in a circle. Find the radius of the circle Circle O is inscribed in ~PQR. PQ = 8, QR -- 11, and PR = 17. Find PT. T 12 Q R 13 Two circles with radii 9 cm and 6 cm are 2 cm apart. Find the length of the common internal tangent A regular pentagon is inscribed in a circle with radius 10. Find the length of a minor arc cut off by one of the diagonals of the pentagon A trapezoid with bases 12 and 20 is inscribed in a semicircle. Find the length of each leg. 15

3 Name Class - Date _ Test 10 Series 3 16 Find the slope of the tangent to at point P[2, 6l 16_ 17 Find the shaded area of the circle if ~ has measure 60 and length 4~ If ~ bisects ~-C, find EC PT, PR are tangent to (~)Q. PT = 3½ (~)Q has radius 12. Find the distance from point P to the circle. (not to the center) 2O Write a proper equation and sol~e for x. 4 2O Copyright McDougai, L ttell & Comp~n~" Test 10 I 215

4 Name Class Date CIRCLES (continued) Test 10 S~,ries 3 Part III (10 points) In problem 21, write a paragraph proof. 21 Given: (~)0 AB ~ CD Prove: z~acw ~ ~DBW 21 C B In problems 22-23, refer to the diagram and the information given. P-T is tangent at T. LBOC ~LAQB ~LP 22 If mb--c = 20, find 23 If mb~= 30, find" m~-~ Make a conjecture about ma---t for various measu~res given for ~-~. Then justify your conjecture. 24 P

5 Name CIRCLES Quiz 2 Series 3... Use after Section 10.4 Given a circle with a diameter of 20. How far from the center is a chord whose length is What is the radius of a circle inscribed in a triangle? Quadrilateral QUAD is circumscribed about a circle. If QU = 19, UA = 12, and AD = 15, what is the measure of QD? Two tangent segments both have a length of 12 and form a 60 angle where they meet at P. How far is P from the circle? Two concentric circles have radii 6 and 8. Find the length of a chord of the larger circle that is tangent to the smaller circle. The centers of two circles with radii 2 and 5 are 8 units apart. Find the length of the common external tangent segment. In the circles described in problem 6, find the length of the common internal tangent segment. 8 Given points T, V, W, X, Y, and Z on a circle. How many chords whose endpoints are two of the given points can be drawn? 9 PX has a length of 8 and is a tangent segment of circle O. If the area of circle O is 25~r, find sin LPOA. A

6 Name CIRCLES Class ~ Date Quiz I Series 3 Use after Section 10.4 The diameter of a circle has endpoints at (3, 1) and (11, 7). How far from the center is a chord whose endpoints are [2, 4) and (7, 9)? Find the length of the chord to the nearest tenth. 2 3 Find the radius of a circle inscribed in a triangle. Quadrilateral QUAD is circumscribed about a circle. If QU = 17, UA -- 12, and AD = 15, find QD. 4 Two segments tangent to a circle form a 60 angle where they meet at point P. Each segment has length 6. How far is P from the c~cle? Two concentric circles have radii of 5 and 8. Within the larger.circle is a chord that is tangent to the smaller circle. What is the length of that chord? 6 7 The centers of two circles with radii of 3 and 5 are 17 units apart. Find the length of the common external tangent. In the circles for problem 6, find the length of the common internal tangent segment. Given points A, B, C, D, E, F, and G on a circle. How many chords whose endpoints are two of the given points can be drawn? Isosceles triangle ABC with base ~-C is inscribed in circle O such that AB = 10. If D is the midpoint of ~ and OD = 2, write a single quadratic equation in x (using x for the radius) that could be solved to find the radius.

7 Name, Class _ Date CIRCLES Quiz 3 seri-es 3 " " Use after Section 10.5 Refer to the diagram and the information given. Given: QO diameter tangents BF and CF secants PE, PD, and PC mldoc = 78 mldre = 82 mb--~ = 90 D G 1 Fin)t mlbfc. 2 Find mlcbf. 3 Find IIID~. 4 Find 5 Find mldpc. 6 Find mlbec. 7 Find mldrc. 8 Find P 3 2_ _ 7 8_ 9 Find mlema. 10 Find mlocb. 10_ 448 Ouiz 3 Copyright McDougal, Littetl & Company

8 Name Class _ Date CIRCLES Quiz 4 Series 3 Use aft~ Section 10.5 A circle with a diameter of 52 has a chord with endpoints at (19, 17} and (-5, 10}. To the nearest tenth, how far from the center is the chord? Given a circle with a diameter o~ 12. From point P, a tangent is drawn to intersect the circle at point A. If PA = 12, how far is P from the circle? 3 Given: (~)O, ~-~ = [4x + 20) ~ ~ = (6x 10) Find mf.dol. D G 4 A central angle intercepts an arc that is ~ of the circle. Find the measure of the angle between the radius drawn to one endpoint of the arc and the chord of the arc. 4 5 The centers of two circles with radii of I and 10 are 15 units apart. Find the length of a common external tangent segment. 6 In the diagram, find the value of the tangent of LA. (continues)

9 Name -- Class Date CIRCLES (continued) Quiz 4 S_eries 3, Use after Section In the diagram, solve for x to three significant digits, x[~~ 7 8 The perimeter of a rhombus is 40 and the longer diagonal is 16. Find, to the nearest degree, the measure of the angle formed by a side of the rhombus and the longer diagonal. 9 Find the value of the tangent of 30. Use the two diagrams at right for problem The area of any tyiangle can be found by taking one half the product of,any two sides and multiplying the answer by.the sine of the included angle. A (Azx =½ab- sinc) For example, in ~ABC, A~ = -12(AC)(AB) sina = (5)(13) ~ =30 N Find the area of ~JIX I Quiz 4 Copyright McDougal, Littell & Company

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11 Name - Class. Date - CIRCLES (continued) Quiz 4 Se~es 3... Use after Section In the diagram, solve for x ~ to three significant digits. ~ 8 The perimeter of a rhombus is 40 and the longer diagonal is 16. Find, to the nearest degree, the measure of the angle formed by a side of the rhombus and the longer diagonal. 8 9 Find the value of the tangent of 30. Use the two diagrams at right for problem The area of any triangle can be found by taking 0~te half the product of.any two sides and multiplying the answer by the sine of the included angle. (A~ = ½ab. sinc) For example, in ~ABC, Aa = ½(AC)(AB) sina = ½(5)(13) Find the area of ~JIX. 4 lo 450 Quiz 4 Copyright McDougal, Lit tell & Company

12 Class Date _ CIRCLES Quiz 5 Series 3 Use after Section 10.7 In problems 1-3, refer to the diagram and the information given. Given: Three tangent circles A, B, and C. AB = 8, BC = 12, and AC = 14. Find the radius of circle A. Find the radius of circle B. Find the radius of circle C. 4 Given a circle with a radius of 15. How far from the center is a chord of length 24? 5 Two circles have radii of 10 and 5. Their centers are 18 units apart. Find the length of the common internal tangent.!n the circles for problem 5, find the length of the common external tangent. 7 In the diagram, find mla. 8 BCDE is an inscribed parallelogram. H BC = 6 and CD = 8, what is the radius of the circle?!f an inscribed angle and a central angle of a circle intercept the same arc, what is the ratio of the central angle to the inscribed angle? 10 How many common tangents do two concentric circles have? 10_

13 ~sme Class _ Date _ CIRCLES Quiz 5 Series 3... Use after Section 10.7 In problems 1-3, refer to the diagram and the information given. Given: Three tangent circles A, B, and G. AB = 8, BC = 12, and AC = Find the radius of circle A. 2 Find the radius of circle B. 3 Find the radius of circle C. 4 Given a circle with a radius of 151 How far from the center is a chord of length 24? 5 Two circles have radii of 10 and 5. Their centers are 18 units apart. Find the length of the common internal tangent. 6 In the circles for problem 5, find the length of the common external tangent. 7 In the diagram, find mla. 6 7_ BCDE is an inscribed. parallelogram. If BC = 6 andcd = 8, what is the radius of the circle? If an inscribed angle and a central angle of a circle intercept the same arc, what is the ratio of the central angle to the inscribed angle? How many commo n tangents do two concentric circles have? 10. Copyright McDougal, LitteB & Company Quiz 5 I 451

14 Name _ Class Date CIRCLES Quiz 6 Ser~es 3... "- Use after Section 10.8 i Solve for x. 2 Solve fory. 3 Solve for z. 4 Solve for w. (continues)

15 Name Class Date _ CIRCLES (continued} Series 3 Use after Section Two secants drawn to a circle from an external point intercept arcs that are, respectively, ~ and ~ of the circle. Find the measure of the secant-secant angle. 6 In circle O, find the length of the altitude to AB. 7 Given a quadrilateral with angles of 100, 70 ~, 80, and 110. If the four degree measures are selected in random order, what is the probability that the resulting quadrilateral can be inscribed in a circle? In the circumscribed polygon, find the length of the missing side A chord-chord angle intercepts a semicircle and its vertical angle intercepts an arc equal in degrees to the arc cut by one side of a regular inscribed pentagon. Find the measure of the chord-chord angle. In problem 10, write A for always, S for sometimes, or N for never. 10 If an arc of a circle is doubled, then the chord of the new arc is twice as long as the chord of the original arc. 10 i McDougal, Littell & Company ~,... i...

16 Name_ Class Date CIRCLES Quiz 7 Series 3 Use after Section 10.8 A tangent line intersects a circle at (8, 4). If the circle has its center at (- 2, 8), what is the equa.tion of the tangent line? Write your answer m general linear form. Given: m~ = 72 md-c = m/_ CPB Find mlapb. A B 3 C A chord 24 inches long is 9 inches from the center of a circle. Find the length of a chord of the same circle that is 7~ 1 inches. from the center. 4 A circle is inscribed in the isosceles trapezoid. The longer base is 20 inches and each of the congruent legs is 16 inches long. Find the diameter of the circle. Given: Diagram as shown BC = DF = 2 ~ LBCG = 30 ~ Find DE. A 6 Two pipes are bound tightly together with a very thin wire as shown. The radii of the pipes are 2 inches and 6 inches. Neglecting any practical allowances for securing the wire, etc., determine the minimum length of the wire. B C (continues)

17 Class Date _ (continued) Quiz 7 Ser-ies 3 " " Use after Section A triangle with angles in the ratio 5:6:7 is inscribed in a circle. At the vertices of the triangle, tangents are drawn to form a circumscribed triangle. Find the angles of the circumscribed triangle. Given: m~ = 120 mldec = 40 Find mlbuc. E A~D~C [ 9 10 Two circles intersect at A and B, with the common chord, ~, of length 10. The segment joining the centers intersects the circles at P and Q. If PQ = 3 and the radius Of one of the circles is 13, what is the radius of the other? Given: A~ is a diameter. AB = 8 AQ= 4 PQ = 12 Find PB. Q~PIo Copyright McDougal, Littelt & Company Quiz 7 I 455

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19 Chapter 9 Part I The Phythagorean Theorem (14 points) 115 2? 3 5~v/~ ~ "x/~ 10 4~ ~ ~v/~ 14 36~v/~ Part II (36 points) obtuse ~/~ 20 ~8~ 21 ~ ~ 23 5~-~ 24 4~/~ 25 h =~, I =13 26 x = ft 28 ~ cm 32 10cm 33 ~169ft Chapter 10 Circles Part I Part II (20 points) I k/~ 9 4½ 10 4~-~ ~r!20 points) ~ ~r 15 4V~ "a ½ 20 x = 3 Part III (10 points) 21 (~)O AB~CDI_~ ~ ~ ~-~ ~ ~l~ ] ~ ~-~j AC ~ BD ---> A--~ ~ ~-~ Also, LA ~ LD and LC ~ L~ (inscribed ang~, so ~A~W ~ ~DBW (ASA), AT is 90~ for any BC,0 < BC <90 Proof: ~LB~= x, then AB =~ ~Q = 180-2x. mlp=x = AT-(180-2x- AT).2 2x =2AT+2x-180 2AT = 180 AT = 90 ~ Chapter 11 Area Part I (5 points) 1N 2A Part II (39 points) 6 324~r 12 48N/~ 147 ~- 18 ~- "V ~ 3S 4N 5A N/~ a = ½ $ ~ 20 27~ (-7,1) [ Answers to Tests 9-11 Copyright McOougal, Littell & Company

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